MATLAB simulation based study on poliovirus sensing through one-dimensional photonic crystal with defect

The present work, theoretically examined the poliovirus sensor model composed of one-dimensional photonic crystal with defect. The transfer matrix method with the help of MATLAB software has been used to detect poliovirus present in the water sample. The main objective of the present work is to design an efficient sensor by identifying the minute variation in the refractive index of water sample due to change in the poliovirus concentration present in the sample. The alternate layers of aluminum nitride and gallium nitride has been taken to realize Bragg reflector having defect layer of air at center of the Bragg reflector. The effect of change in thickness of defect layer region, period number and incident angle corresponding to transverse electric wave has been examined to optimize the structure which correspond maximum performance of the proposed poliovirus sensing structure. The maximum performance of the structure has been obtained with optimum value of defect layer thickness 1200 nm, period number 10 and incident angle 40°. Under optimum condition maximum sensitivity of 1189.65517 nm/RIU has been obtained when the structure is loaded with waters sample of poliovirus concentration C = 0.005 g/ml whereas figure of merit, quality factor, signal to noise ratio, dynamic range, limit of detection and resolution values become 2618.28446 per RIU, 3102.06475, 2.27791, 2090.99500, 1.91E−05 and 0.24656 respectively.

Nowadays optical biosensors based on photonics and plasmonics technologies are being extensively used as a most popular tool for sensing and detection of analytes belong to the field of biomedical applications, food safety, chemical engineering and environmental monitoring. The plasmonics biosensors work on the principle of surface plasma resonance (SPR) either by utilizing angle interrogation or wavelength interrogation. Angle interrogation is preferred over wavelength integration because it provides better results like larger signal-to-noise ratio. The interaction of immobile ligands with analytes on the surface of sensing medium due to change refractive index of analyte results significant change in the resonance angle of plasmonics biosensors based on SPR phenomenon. The resent review article of Arun et al. highlights the advances of biosensors based on SPR technologies for which includes SPR based imagining and magneto-optical sensing. This article also highlights the features of some other important optical biosensors which work on the fiber optic phenomenon like evanescent wave, fluorescence evanescent wave and polymerase colorimetric chain reaction. Some other optical biosensors based on interferometry, ellipsometry, enhanced surface Raman scattering phenomenon are also been discussed 1 . Some of the research fellows have investigated the novel way of designing of optical biosensors by utilizing the phenomenon of long-range SPR 2,3 . For example research work of Arun et al. gives an excellent idea of designing a long-range SPR sensor with improved sensing capabilities employing 2D material layer of platinum diselenide (PtSe2) 3 . Apart from the SPR technology based excellent biosensing devices some of the research groups are giving their efforts to design and develop biosensors based on one-dimensional (1d) photonic crystals (pcs) due their feasibility of fabrication, simple architecture, user friendly handling and cost effectiveness.
Photonic structures are the smart composites which could tremendously control the propagation of light due to appearance of novel phenomenon of photonic bandgaps (PbGs). All the frequencies of light incident on www.nature.com/scientificreports/ such structures are significantly attenuated if they fall inside this gap [4][5][6][7] . The photon localization and existence of PbG are amongst the peculiar properties associated with the photonic structures 8,9 . The ease of designing and fabrication makes 1d photonic structures as a most suitable and promising candidates over two-dimensional (2d) and three-dimensional (3d) structures 10 . Any deformation in the periodicity of such structures may result appearance of resonant tunneling mode inside PbGs which can be easily relocated inside PbG either by changing the refractive index or by changing the thickness of defect layer region theoretically as well as experimentally 11,12 . Thus the deformation in the periodicity of photonic designs may enhance the novelty in comparison to that of perfect ones which have attracted the optical and physical societies for the development of various sensors with remarkable relevance in optical, chemical, physical and biomedical applications 13 . Such aperiodic structures are called as defective photonic crystals (dpcs) 14 . The sensing and identification capabilities of dpcs have opened new gateway for the development of various sensors like biosensors, salinity sensor, chemical sensor, pressure sensor and magnetic sensor which have their usefulness in wide range of biological, chemical, medical and environmental applications [15][16][17][18][19] . This usefulness is due to their excellent set of properties like higher sensitivity, quick response time and large quality factors 20,21 . The most of the applications discussed above are based on the movement of resonant mode inside PbG due to variation in the refractive index of defect layer region in presence of specific external environment like concentration, temperature, magnetic field and pressure 22,23 . In particular, the refractive index sensing may be the cornerstone for identification and detection of various samples depending upon their physical, biological and chemical properties 12,24 . The present study is based on theoretical examination of the transmission properties of 1d dpc loaded with water sample containing poliovirus with the help of MATLAB software. The objective of this research work is to develop a cost effective alternative sensor composed of 1d dpc for detection poliovirus sensor because it destroy the nerve cells and may become root cause of acute flaccid paralysis (AFP) 25 . The intention of the present work as per our believe is to develop a simple and new method involving low fabrication cost in comparison to the conventional methods like cell culture, intratypic differentiation, genome sequencing, serology for poliovirus diagnostic 26 . The results of these traditional methods have poor stability, lower accuracy, high cost and required specific environmental conditions during investigation process 27 . On the other hand the present work only deals with the change in the properties of resonant mode due to change in the refractive index of poliovirus sample. The cornerstone of the work presented here deals with the refractive index variation of water sample due to change in its poliovirus concentration. Any minute variation in the refractive index of the sample is immediately sensed by relocating the position of resonant peak inside PbG of the sensor. The numerical results of this work are based on transfer matrix method and change in the refractive index of water dependent upon the poliovirus concentration.
The organized of the manuscript is as under: the poliovirus sensor design and structural formulation of the work are briefly discussed in "Structural design and its realization" and "Description of poliovirus solution". The results and discussions pertaining to the poliovirus sensor are presented in "Results and discussions". Finally we have discussed the conclusions in "Conclusions".

Structural design and its realization
The proposed poliovirus sensor has been made by using 1d defective photonic crystal (AB)ND(AB)N as shown in Fig. 1 below.
The letters A, B and D have been used to represent materials Aluminum nitride (ALN), Gallium nitride (GaN) and air cavity of the proposed design respectively 28,29 . The air cavity region D of the structure is utilized for investigating various poliovirus samples poured into D. The spectral dependence of refractive indices of aluminum and gallium nitride materials in the infrared region of spectrum has been defined with the help of Eqs. (1) and (2) respectively as 28,29 (1) Here n A and n B are representing refractive indices of aluminum and gallium nitride materials respectively. The free space wavelength is measured in nanometers. The thickness of layers A, B and D are taken to be d A = 100 nm, d B = 150 nm and d D = 800 nm respectively. The period number N of the structure has been initially selected as 9 to begin with simulation work.
There are several fabrication techniques that can be used for realization of such defective photonic structures. The materials choice is very essential for identifying the most suitable fabrication technique to realize such structures like dip coating, sol-gel method etc. The fabrication of multilayer periodic structures made up of materials like nanocomposite, polymers, and dielectrics can be easily realized by using a process of spin coating. In this process first we apply precursor solution over the flat substrate, the evaporation of the solvent from the substrate is done by initiating the spin process. Next annealing protocol is applied for solicitation of the layer on the substrate. The remaining stacks of layers are being deposited one over the other by repeating above mentioned sequence of various steps involved in the deposition of layers. During the deposition of various layers we also control the thickness of each layer of the stack by either monitoring the concentration of cast solution or by controlling the rotational speed. After fabricating the structure one can use standard elliposmetric spectroscopic methods dependent upon angle for characterization of the fabricated structure.

Description of poliovirus solution
The refractive index of the contaminated water with poliovirus (n pv ) dependent upon the various poliovirus concentration levels (C) measured in g/ml present in the water is defined in Eq. (3) as 30 Here n w is representing refractive index of pure water (1.33) and a is the specific refractive index of water contaminated with poliovirus of specific concentration level 0.174 ml/g. In the present research work the concentration level C of the virus has been varied from 0.001 to 0.05 g/ml in steps of 0.001. All the concentration dependent refractive index values of water contaminated with poliovirus has been presented in Table 1 below. These values have been extracted from Eq. (3).
Computational model. In the present design we have considered 1d Bragg reflector whose periodicity has been broken by considering a defect layer of air at the centre of Bragg reflector to get modified 1d dpc (AB) N D(AB) N as discussed above in Fig. 1. All the layers of the proposed poliovirus sensing structure are deposited over a glass substrate of refractive index n S . The surrounded medium around whole structure is air. The plane polarized light whose electric field wave vector is normal to plane of incidence is allowed to enter into the 1d dpc (AB) N D(AB) N at an incident angle θ with normal to the senor from air 31 .
The transfer matrix is used here for describing the interaction between the incident light with the proposed structure as 32 Here transfer matrix elements are being represented by C 11 , C 12 , C 21 andC 22 . The period number is shown by a letter N. The interaction between incident S polarized light with proposed poliovirus sensor is studied by TMM. There are many articles in which details of TMM can be found. The interplay between proposed sensor and S polarized can be defined with the help of following matrix as 33 The subscript j is used to represent layers A, B and D of the structure (j = A, BandD). For S polarized incident light one can define q j as q j = n j cosγ j . Here phase difference in each layer of the sensor is denoted by γ j as Here the index of refraction, thickness and ray angle inside j layer of the poliovirus sensor are represented by n j , d j and θ j respectively.
One can easily obtained the coefficient of transmission t of proposed poliovirus sensor by using the relation as under 33 Here notations q 0 = n 0 cos θ and q S = n S cos θ S are being used to represent phase differences associated with light wave in incident and exit media respectively for TE polarized wave.

Results and discussions
With the help of theoretical formulation discussed above we have developed MATLAB code for evaluation of transfer matrix of the structure (AB) 9 D(AB) 9 which in turn provides the transmission characteristics and other relevant plots pertaining to the proposed work. First the simulations has been initiated by pouring a water sample of refractive index 1.33 into the air cavity reason D of the structure and allow a light to enter into the structure normally. The entire simulation work has been carried out in the infrared region of electromagnetic spectrum ranging from 1190 to 1590 nm. Figure 2 below shows the transmittance of the structures (AB) 18 without cavity layer D and (AB) 9 D(AB) 9 with cavity layer D loaded with water sample of refractive index 1.33. Figure 2 contains two transmittance plots corresponding to structures without and with cavity layer D loaded with water sample in red and black colour solid lines respectively. The transmittance plot of the structure (AB) 18 shows PBG located between 1240 and 1485 nm. The introduction of cavity layer D into the middle of one dimensional multilayer periodic structure (AB) 18 is responsible of the creation of 1d defective photonic crystal structure (AB) 9 D(AB) 9 as shown in Fig. 1. This modification ensures the appearance of discontinuous electromagnetic radiations of specific wavelength knows as resonant mode or defect mode inside PBG of 1d dpc. The presence of resonant mode inside PBG of 1d dpc is due to the break in periodicity of the structure. The transmittance plot shown in black solid line in Fig. 2 is representing the PbG of 1d dpc (AB) 9 D(AB) 9 in addition to resonant mode of unit transmittance located at wavelength 1337.7418 nm inside PbG. In this research work we have explored the biosensing capabilities of the defect mode inside PbG associated with 1d defective pc for the sensing and detection of poliovirus present in the water sample.
Reflectance spectra of 1d dPhC (AB) 9 D(AB) 9 loaded with water samples of low concentration. In all the reflectance calculations of the 1d DPC (AB) 9 D(AB) 9 the thickness of layers A, B and D are initially taken as d A = 100 nm, d B = 150 nm and d D = 800 nm respectively. Figure 3 below shows the reflectance of 1d DPC (AB) 9 D(AB) 9 loaded with water samples containing poliovirus of low concentration level as 0.002 g/ml, 0.005 g/ml, 0.007 g/ml, 0.010 g/ml, 0.012 g/ml, 0.014 g/ml, 0.016 g/ml, 0.018 g/ml and 0.020 g/ml with respect to pure water sample of concentration 0 g/ml. In this study normal incidence has been taken and period number is fixed to 9. It is evident from Fig. 3 that as concentration of poliovirus present in the water sample increases the defect mode associated with each water sample shifts towards higher wavelength side. This variation does not have any significant impact on the full width half maximum of each defect mode. It is almost stagnant.
The change in the position of defect mode inside PBG of 1d DPC (AB) 9 D(AB) 9 loaded with water samples containing poliovirus of low concentration levels as 0 g/ml, 0.002 g/ml, 0.005 g/ml, 0.007 g/ml, 0.010 g/ml, 0.012 g/ml, 0.014 g/ml, 0.016 g/ml, 0.018 g/ml and 0.020 g/ml are being shown in Fig. 4 below. The change in refractive index of water samples leads to the shifting of defect mode position towards higher wavelength side. Figure 4 shows the linear curve fitting between the positions of poliovirus concentration and the central wavelength of defect mode shown in solid red balls. This linear curve fitting provides a solid red line of slope 60.947 nm/g/ml representing an average sensitivity of our poliovirus sensor as per the following equation  9 loaded with water samples containing poliovirus of low concentration level as 0.002 g/ml, 0.005 g/ml, 0.007 g/ml, 0.010 g/ml, 0.012 g/ml, 0.014 g/ml, 0.016 g/ml, 0.018 g/ml and 0.020 g/ml with respect to pure water sample of concentration 0 g/ml.  www.nature.com/scientificreports/ Here D is the change in defect mode position due to change in the refractive index of analytes ( n ). The symbols D FWHM are representing central wavelength of defect mode and its full width half maximum respectively.
Further we have evaluated the performance of proposed 1d DPC (AB) 9 D(AB) 9 loaded with poliovirus solution of different concentration which varies from 0 to 0.05 in steps of 0.001. The purpose we have fulfilled by examining the sensitivity and quality factor of the proposed design loaded with all poliovirus solution as per the data given in Table 2. The data of Table 2 reflects that as the concentration of the poliovirus present in the water sample changes from 0 to 0.050 g/ml in steps of 0.001 the sensitivity of the sensor varies between minimum of 344.8275862 nm/RIU to maximum of 351.2901712 nm/RIU. The variation of quality factor varies between 977.4712949 and 998.7525992 when the concentration of the sample loaded into the structure varies from 0 to 0.05 g/ml. Figure 5 presents the linear curve fitting applied between the refractive index of various poliovirus samples of concentrations 0-0.050 g/ml loaded into the structure and their respective defect mode positions. The slope of line plotted by applying linear curve fitting over the refractive index of poliovirus samples and defect mode positions data as shown in Table 2 refers the average sensitivity of 351.28 nm/RIU of our sensing structure according to the following relation as Effect of concentration of poliovirus present in the water sample on the sensitivity. According to Eq. (3), the refractive index of water sample contaminated with poliovirus can be directly altered by increasing the concentration of poliovirus present in the sample 30 . The impact of changing the concentration from 0 to 0.05 g/ml on the sensitivity of the proposed sensor composed of 1d DPC will be studied here. Figure 6 shows the sensitivity variation of the proposed structure at different values of concentration level C form 0 to 0.05 g/ml as evident from Table 2.
Initially with increase of C from 0 to 0.005 g/ml, the sensitivity of proposed sensor increases from 344.8275862 to 350.6896552 nm/RIU due to movement of defect mode associated with the sample towards higher wavelength side as evident from Table 2. Further increase in the value of C results some modulated variations of sensitivity which are limited between 348.0842912 and 351.2901712 nm/RIU. These sensitivity variations of our design are very close to average sensitivity value of 351.28 nm/RIU obtained from liner curve fitting as discussed above in Eq. (9).
Efficiency analysis of the proposed sensor. We have further analyzed the efficiency of proposed sensor composed of 1d DPC (AB) 9 D(AB) 9 with the help of signal-to-noise ratio, limit of detection and resolution limit. The major factor which influences the performance of any sensing structure is the ratio between signal-to-noise and abbreviated as SNR. In designing of any sensor it is always curtail to have smaller full width half maximum (FWHM) and larger SNR values. The following relation can be used to calculate SNR values of the proposed sensor with the help of Table 2 as 36 The finest measurable refractive index variation of the sample is known in terms of limit of detection (LoD). The smallest LoD value of our poliovirus sensor with d D = 2000 nm is recorded as 7.16E−05. The LoD values of our structure can be obtained from the following relation by using the data of Table 2 as 37 The ability of the poliovirus sensing structure to notice the smallest movement of defect mode inside photonic band gap due to change in the refractive index of the poliovirus sample is defined as resolution limit (RL) and can be calculated by using the following relation as 38 The change in sensitivity parameter of the poliovirus sensor with respect to change in the full width at half maximum (FWHM) of sensor due to change in analyte is defined as another characteristic parameter called as the figure of merit (FOM). It is defined as 38 The ratio of central wavelength of defect mode with square root of FWHM is measure of dynamic range (DR) of present poliovirus sensor. It is unit less parameter which is defined as 38 www.nature.com/scientificreports/ Table 2. Performance evaluation of 1d dpc (AB) 9 D(AB) 9 loaded with poliovirus solution of different concentration in terms of sensitivity and quality factor. www.nature.com/scientificreports/ Optimization of the thickness of defect layer. In addition to sensitivity and quality factor as defined Eqs. (10) and (11), we have included more parameters as defined in Eqs. (13)- (17) for the efficiency analysis of proposed 1d DPC (AB) 9 D(AB) 9 loaded with sample of concentration C = 0.005 (n pv = 1.33087). These parameters have been taken as a key factor for optimizing the performance of the structure under the effect of change in the thickness of defect layer, change in period number of the structure and change in angle of incidence. In this analysis we have varied the thickness of defect layer region form d D = 800 nm to d D = 12,000 nm. The effect of change in thickness of defect layer on the performance evaluating parameters of the structure as defined in previous equations have been recorded in Table 3 below. Figure 7 depicts the dependence of the sensitivity and full width half maximum versus thickness of the defect layer region. Specifically, when the thickness of defect layer thickness increases from 800 to 12,000 nm, the sensitivity of sensor gradually increase from 350.6897 to 948.2759 nm/RIU while FWHM of defect modes associated with the sensor decreases from 1.3660 to 0.2225 nm. For defect layer thickness higher than 12,000 nm, the defect mode moves out of PBG and  Table 2 and red solid line is representing linear curve fitting data. www.nature.com/scientificreports/ new defect mode appears into the PBG which have compromised values of both sensitivity and FWHM. The maximum sensitivity value of 948.2759 nm/RIU is achieved when the defect layer thickness of the sensor is set to d D = 12,000 nm. So, the defect layer thickness of 12,000 nm is considered as an optimized thickness of structure. Under optimized cavity thickness the FWHM attains its minimum value of 0.2225 nm as required. Moreover this optimized defect layer thickness also improves the interaction between incident light and poliovirus sample due to the increase in the geometrical path difference between the light inside cavity which results significant enhancement in the sensitivity of the sensor. Figure 8 shows the numeric values FoM and QF of the proposed 1d DPC (AB) 9 D(AB) 9 loaded with sample of C = 0.005 g/ml at different defect layer thickness considerations from 800 to 12,000 nm. It appears from Fig. 7 Table 4 below.

Effect of change in thickness of defect layer on FoM and Q factor.
Effect of change in period number of the structure Non S and FWHM. Figure    www.nature.com/scientificreports/ Effect of change in period number of the structure SNR on DR. Figure 13 indicates that as period number of the structure changes from N = 5 to N = 10, the signal-to-noise ratio and dynamic range starts to increase. Both the values of SNR and DR become maximum of 6.5981 and 3972.0829 respectively with N = 10. Optimization of angle of incidence. After obtaining optimized values of defect layer thickness d D and period number N of the proposed poliovirus sensor as a 12,000 nm and 10 respectively, we have extended our efforts to further improve the performance of the proposed design by changing the incident angle from θ = 0° to θ = 40°corresponding to TE wave. The change in the incident angle is one of an effective way of controlling and enhancing the performance of any sensor due to increase in the path length of the incident light into the sensor.   Table 5 below. The variation in incident angle affects the defect mode position inside PBG of the structure. Figure 15 below shows the variation of sensitivity and full width half maximum of 1d DPC (AB) 9 D(AB) 9 loaded with the sample of refractive index 1.33087 with d D = 12,000 nm on the incident angle θ corresponding to TE wave. It shows that the sensitivity and FWHM of the sensor increases with increase in the incident angle from θ = 0° to θ = 40°. For incident angles higher than 40° defect mode disappears.

Effect of change in angle of incidence on S and FWHM.
Effect of change in angle of incidence on FoM on QF. Figure    www.nature.com/scientificreports/    Effect of change in angle of incidence on SNR and DR. Figure  Effect of change in angle of incidence on LoD and RS. Finally, the pictroial representation of LoD and RS dependent upon incident angle has shown in Fig. 18 below. It shows that any increase in the incident angle from 0° results signifcant increase in both these values. At θ = 40°, LoD and RS values become 1.91E−05 and 0.24656. These values are still small as desired. Finally with the above analysis we have successfully optimized our sensor design for detection of poliovirus present in the water sample under consideration. The optimum values of defect layer thickness, period number and incident angle corresponding to TE wave are obtained as 1200 nm, 10 and 40° respectively. The selection   www.nature.com/scientificreports/ of these optimum parameters associated with our structure makes the structure highly sensitive. The numeric value of sensitivity becomes 1189.65517 nm/RIU when the structure is loaded with sample of concentration C = 0.005 g/ml.
For providing better picture of the proposed work we have compared the proposed work with the work reported by other in recent years. Table 6 summarizes the comparison of performance between the structures proposed by us and other researchers in present years in terms of publication year of work, structural topology, sensitivity, figure of merit and quality factor. As evident from structures reported in references [39][40][41] all have PbG topology, structures reported in reference 42 is based on plasmonics toplogy as well. The structures based on photonic, plasmonics and combination of both topologies have their advantages and disadvantages pertaining to the biosensing applications 41 . The transmission properties of the works presented in Table 6 are based on PbG. The structures whose transmission properties are based on PbG are good candidates for biosensing applications due to two main reasons. First, the edges of the PbG are sharp and second due to wider band gap for accommodating large number of analytes. The overlapping between high and low PbG due to change in the refractive index of analyte is one of major issue which must be addressed before using pc as a biosensor. For this reason the proposed work is being carried out in the near infrared region of the spectrum which is most suitable for biosensing applications. Due to the consideration of all above key points S, FoM and QF values of proposed photonic biosensor are exceptionally good and make our biosensor most sensitive and efficient as evident from comparison Table 6.

Conclusions
In this paper, a poliovirus sensor has been proposed for detection of virus concentration present in the sample by means of based on 1d dppc. The transmission spectra of this study have been obtained by using MATLAB software in addition to TMM. The contaminated water containing poliovirus sample is poured into the defect layer region of 1d dpc which shifts the location of defect mode from one position to another position inside PbG due to variation in the refractive index of water sample dependent upon the concentration levels of poliovirus present in the sample. The proposed sensing structure has been optimized to strengthen the sensing capabilities of the sensor by considering the effect of change in transmission spectra due to change in (1) defect layer thickness, (2) period number of the structure and (3) incident angle corresponding to TE wave. The adoption of these three approaches may bring the maximum sensitivity of 1189.65517 nm/RIU from the structure when the sensor is loaded with sample of concentration 0.005 g/ml. Though for achieving maximum sensitivity we have to tolerate with other performance evaluating parameters of the sensor, this compromise is not significant in comparison to the enhancement obtained in sensitivity.

Data availability
The data that support the findings of this study are available from the corresponding author upon reason-able request.  Table 6. Comparison between the performances of present and earlier reported sensing works based on sensitivity, figure of merit and quality factor. N.C. not calculated Significant values are given in bold.